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This statement was implemented in value function , the fi rst central element of prospect theory.
The emphasis on changes as the carriers of the value should not be taken to imply that the value
of a particular change is independent of an initial position. Value should be treated as a function
of two arguments: the asset position that serves as a reference point and the magnitude of the
change from the reference point. In other words value function represents the outcomes expected.
Speaking broadly about value function, it has an s-shape characterized by the following
features:
• It is defi ned on deviation from the reference point.
• It is concave in the domain of gains, favouring risk aversion.
• It is convex in the domain of losses, favouring risk seeking.
• It is sharply kinked at the reference point, and loss-averse - steeper for losses than for gains
by a factor of about 2-2, 5.
The last point argues that deterioration that an individual expects in losing a sum of money is
bigger than the pleasure associated with gaining the same amount. As the evidence shows, most
people fi nd a symmetrical situation in which they can lose or gain the same amount with the
same probability distinctly unattractive. Another central component of prospect theory is
weighting function which transforms single probabilities into decision weights. The original version
of the theory with transformation in weighted function implies violations of fi rst-order stochastic
dominance. That is, one prospect might be preferred to another even if it yielded a worse or
equal outcome with the probability prospect. This disadvantage has motivated the development
of cumulative prospect theory variants which uses transformation of cumulative probabilities
rather than single probabilities. Theoretical results in the fi eld of reference-dependence in
cumulative prospect theory are obtained by Schmidt (2004).
The weighting function proposed by Kahneman (1979) satisfi es overweighting and
subadditivity for small values of p , and subcertainty and subproportionality. As a fact, subpropor-
tionality together with the overweighting of small probabilities imply that p is subadditive over
all ranges (0, 1).
The basic formula of the theory of choice of Kahneman and Tversky in the simplest form
combines value function v and weighting function p in order to determine the overall value.
It is assumed for the evaluation phase and given by:
V ( x 1 , p 1 ; x 2 , p 2 ) = p ( p 1 ) v ( x 1 )+ p ( p 2 ) v ( x 2 ),
where x 1 and x 2 are potential outcomes; p 1 and p 2 their respective probabilities; ( x 1 , p 1 ; x 2 , p 2 ) is a
regular prospect (either p 1 + p 2 <1 or, x 1 ≥ 0 ≥ x 2 or x 1 ≤ 0 ≤ x 2 ).
This theory, which constitutes a good complement to CCB, solves some of the main frailties
of the original models, offering new paths for tourism research. General reasons for CCB frailty
and the advantages of prospect theory are comparatively analyzed in the following section.
New frontiers in tourism research
In order to clearly state the advantages of prospect theory compared with CCB, a number of
assumptions, implications and consequences of CCB were recovered in order to compare them
with the results of Kahneman and Tversky. They will be the main points of our discussion
of differences and possible links between the classical theory of consumer behaviour and
prospect theory.
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